Recent advances in low-dimensional materials have enabled the synthesis of single-walled carbon nanotubes encapsulated in hexagonal boron nitride (BN) nanotubes (SWCNT@BNNT), creating one-dimensional van der Waals (vdW) heterostructures. However, controlling the quality and crystallinity of BNNT on the surface of SWCNTs using chemical vapor deposition (CVD) remains a challenge. To better understand the growth mechanism of the BNNT in SWCNT@BNNT, we conducted molecular dynamics (MD) simulations using empirical potentials. The simulation results suggest that spontaneous BN nucleation is unlikely to occur on the outer surface of the SWCNT when we assume only vdW interaction between the BN and SWCNT layers. However, we observe the elongation of the BNNT when a short BNNT is provided as a seed nucleus on the SWCNT. This grown BNNT structure, with its sharply cut edges, aligns with experimental observations made using transmission electron microscopy (TEM). Moreover, the edge-reconstruction process favors zigzag B edges, which exhibit low edge energy according to the ReaxFF potential. Our simulation successfully provides insights into the catalyst-free growth process of this one-dimensional vdW heterostructure.